If X and Y are mutually exclusive events, then if X occurs,

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BlackTom AI · Accepted Answer

Question restatement: If X and Y are mutually exclusive events, then if X occurs,

Option 1: 'Y must occur' — This is incorrect. Mutually exclusive events cannot happen together, so if X occurs, Y cannot occur. The fact that X happened directly prohibits Y, rather than requiring Y to happen.

Option 2: 'X and Y are independent' — This is false. Independence means the occurrence of X does not affect the probability of Y. Mutually exclusive events have zero probability of occurring together, which in turn means they are not independent (unless one event has zero probability overall, which is not implied here).

Option 3: 'X and Y are complement' — This is not necessarily true. For events to be complements, they must be exhaustive (together covering the entire sample space) and mutually exclusive. Mutual exclusivity alone does not guarantee that X and Y together cover all possible outcomes; there could be outcomes where neither X nor Y occurs.

Option 4: 'Y cannot occur' — This statement aligns with the definition of mutually exclusive events: if X occurs, Y cannot occur, because the two events cannot happen simultaneously. Since they cannot occur together, the occurrence of X rules out Y.

Summary of the reasoning: Among the options, only the statement that Y cannot occur when X occurs is consistent with mutual exclusivity. The other options misconstrue independence, complementarity, or overstate the relationship, given mutual exclusivity does not by itself ensure exhaustiveness or independence.

If X and Y are mutually exclusive events, then if X occurs,

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